This work consists of applying methods of dynamical systems in complex variables to an applied
problem: nding the roots of an arbitrary polynomial.
Speci cally, we use the iteration z 7! z2 + c to nd the roots of a complex polynomial p(z).
By applying that iteration we can use concepts of complex analysis and linear algebra, such as the
Mandelbrot set and the Vandermonde matrix to tackle our problem.
We see how these ideas have applications in other contexts, such as number theory. We add
the discussion of pseudo code and code written in Python 3, for the sake of doing experiments
that illustrate the di erent sections of this thesis. This discussion let us analyse the computational
complexity of the algorithm on top of the mathematical discussion.
| Identifer | oai:union.ndltd.org:PUCP/oai:tesis.pucp.edu.pe:20.500.12404/21016 |
| Date | 27 November 2021 |
| Creators | Torres Romero, Jesús Stefano |
| Contributors | Poirier Schmitz, Alfredo Bernardo |
| Publisher | Pontificia Universidad Católica del Perú, PE |
| Source Sets | Pontificia Universidad Católica del Perú |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/bachelorThesis |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/closedAccess |
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